Advertisement

Abel Equations and Generalizations

  • Palaniappan Kannappan
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter, Abel’s equation, exponential iteration, associative and commutative equations, trigonometric equations, and systems of equations are treated. Generalizations and connections to information measures are treated. Hilbert, in his famous address to the International Congress of Mathematicians held in Paris in 1900 [372], posed many unsolved problems. The second part of his fifth problem is devoted in general to functional equations and in particular to functional equations treated by Abel, who was the first to treat functional equations systematically. He presented a general method of solving equations of quite general forms. For the most part, he solved functional equations by reducing them to differential equations.

Keywords

General Solution Functional Equation Shannon Entropy Information Measure Fundamental Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterloo ONCanada

Personalised recommendations